FTT model including constraint and learning
Contents
9. FTT model including constraint and learning#
In this notebook the cell magic %latexmodelgrab is used. It allows the specification of segments of the model.
#This is code to manage dependencies if the notebook is executed in the google colab cloud service
if 'google.colab' in str(get_ipython()):
import os
os.system('apt -qqq install graphviz')
os.system('pip -qqq install ModelFlowIb ipysheet --no-dependencies ')
%load_ext autoreload
%autoreload 2
import pandas as pd
from IPython.core.display import HTML,Markdown,Latex
from modelclass import model
import modeljupytermagic
# some useful stuf
model.widescreen()
pd.set_option('display.max_rows', None, 'display.max_columns', 10, 'display.precision', 4)
9.1. Define the segments of the model#
By defining the a model as segments the whold model does not have to be defines in one cell. This simplifies the specification. And debugging.
As many segments will use the lists of technologies, segments which name starts with list will be appended to each segment.
9.2. Changes#
for each sector change demand to production
calculate average cost for power generation
change the cost equations so the cost include learning
9.2.1. First the technologies are defined#
%%latexmodelgrab mftt ndisplay segment=list1
Two lists of technology are defined:
$List \; i =\{Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal\} \\
fosile: \{ 1 , 1, 1, 0, 0, 0, 0, 0 \}$
$List \; j = \{Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal \}$
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
%%latexmodelgrab mftt ndisplay segment=text1
Any number of technology can be specified (limited by the avaiable memory)
The time index $_t$ is implicit.
Any number of technology can be specified (limited by the avaiable memory)
The time index $_t$ is implicit.
9.2.2. Preferences#
%%latexmodelgrab mftt ndisplay segment=preferences
Each technology is compared to all other based on the percieved costs and the preferences (choice likelihood) $F^{i,j}$ are calculated.
For all technologies $F^{i,j}+F^{j,i} = 1 $
\begin{equation}
\label{eq:preferences}
\underbrace{F^{i,j}}_{Preferences} = \frac{1}{
1+exp(
\frac{(Cost\_argumented^{i}-Cost\_argumented^{j})}{\sigma^{i,j}} )}
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
Each technology is compared to all other based on the percieved costs and the preferences (choice likelihood) $F^{i,j}$ are calculated.
For all technologies $F^{i,j}+F^{j,i} = 1 $
\begin{equation} \label{eq:preferences} \underbrace{F^{i,j}}_{Preferences} = \frac{1}{ 1+exp( \frac{(Cost_argumented^{i}-Cost_argumented^{j})}{\sigma^{i,j}} )} \end{equation}
9.2.4. Sigma#
%%latexmodelgrab mftt ndisplay segment=sigma
The percieved width in the choice function
\begin{equation}
\label{eq:sigma}
\sigma^{i,j} = \sqrt{(\sigma^{i})^{(2)} \cdot (\sigma^{j})^{(2)}}
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$ The percieved width in the choice function
\begin{equation} \label{eq:sigma} \sigma^{i,j} = \sqrt{(\sigma^{i})^{(2)} \cdot (\sigma^{j})^{(2)}} \end{equation}
9.2.5. Total Demand#
%%latexmodelgrab mftt ndisplay segment=demand
\begin{equation}
\label{eq:UD_total}
UsefulDemand\_total = UsefulDemand\_total_{t-1} \cdot
(1+\frac{UsefulDemand\_total\_growth}{100})
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
\begin{equation} \label{eq:UD_total} UsefulDemand_total = UsefulDemand_total_{t-1} \cdot (1+\frac{UsefulDemand_total_growth}{100}) \end{equation}
9.2.6. Production#
%%latexmodelgrab mftt display segment=production
The production from each sector can be calculated. The same goes fdor
\begin{equation}
\label{eq:production}
Production^{i} = Share^{i} \cdot UsefulDemand\_total
\end{equation}
\begin{equation}
\label{eq:acc_production}
Production\_accumulated^{i} = Production\_accumulated^{i}_{t-1} + Production^{i}
\end{equation}
The production from each sector can be calculated. The same goes fdor
\begin{equation} \label{eq:production} Production^{i} = Share^{i} \cdot UsefulDemand_total \end{equation}
\begin{equation} \label{eq:acc_production} Production_accumulated^{i} = Production_accumulated^{i}_{t-1} + Production^{i} \end{equation}
do i $
frml <production> Production__{i} = Share__{i}*UsefulDemand_total $
enddo $
do i $
frml <acc_production> Production_accumulated__{i} = Production_accumulated__{i}(-1) + Production__{i} $
enddo $
LIST I = I : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL /
FOSILE: 1 1 1 0 0 0 0 0 $
LIST J = J : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL $
FRML <PRODUCTION> PRODUCTION__OIL = SHARE__OIL*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__COAL = SHARE__COAL*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__GAS = SHARE__GAS*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__BIOMASS = SHARE__BIOMASS*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__SOLAR = SHARE__SOLAR*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__WIND = SHARE__WIND*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__HYDRO = SHARE__HYDRO*USEFULDEMAND_TOTAL $
FRML <PRODUCTION> PRODUCTION__GEOTHERMAL = SHARE__GEOTHERMAL*USEFULDEMAND_TOTAL $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__OIL = PRODUCTION_ACCUMULATED__OIL(-1) + PRODUCTION__OIL $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__COAL = PRODUCTION_ACCUMULATED__COAL(-1) + PRODUCTION__COAL $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__GAS = PRODUCTION_ACCUMULATED__GAS(-1) + PRODUCTION__GAS $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__BIOMASS = PRODUCTION_ACCUMULATED__BIOMASS(-1) + PRODUCTION__BIOMASS $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__SOLAR = PRODUCTION_ACCUMULATED__SOLAR(-1) + PRODUCTION__SOLAR $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__WIND = PRODUCTION_ACCUMULATED__WIND(-1) + PRODUCTION__WIND $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__HYDRO = PRODUCTION_ACCUMULATED__HYDRO(-1) + PRODUCTION__HYDRO $
FRML <ACC_PRODUCTION> PRODUCTION_ACCUMULATED__GEOTHERMAL = PRODUCTION_ACCUMULATED__GEOTHERMAL(-1) + PRODUCTION__GEOTHERMAL $
LIST I = I : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL /
FOSILE: 1 1 1 0 0 0 0 0 $
LIST J = J : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL $
9.2.7. price learning#
%%latexmodelgrab mftt ndisplay segment=endogeneous_prices
The price of new technology falls in line with its accumulated use through a number of effects.
In princip it depends in global accumulated production. But lacking the data, we just use the local accumulated production. There are many
possible functional forms. This is just one example.
\begin{equation}
\label{eq:change_production}
Change\_accumulated\_Production^{i} = \frac{Production\_accumulated^{i}}{Production\_accumulated^{i}_{t-1}}
\end{equation}
\begin{equation}
\label{eq:price_impact}
Cost^{i} = Cost^{i}_{t-1} \cdot (Change\_accumulated\_Production^{i})^{(-cost\_elasticity^{i})}
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
The price of new technology falls in line with its accumulated use through a number of effects.
In princip it depends in global accumulated production. But lacking the data, we just use the local accumulated production. There are many possible functional forms. This is just one example.
\begin{equation} \label{eq:change_production} Change_accumulated_Production^{i} = \frac{Production_accumulated^{i}}{Production_accumulated^{i}_{t-1}} \end{equation}
\begin{equation} \label{eq:price_impact} Cost^{i} = Cost^{i}_{t-1} \cdot (Change_accumulated_Production^{i})^{(-cost_elasticity^{i})} \end{equation}
9.2.9. Argumented cost#
%%latexmodelgrab mftt ndisplay segment=Argumented_cost
\begin{equation}
\label{eq:Z_costbarrier}
Cost\_argumented^{i} = Cost^{i} + penalty\_max\_l^{i} - deduction\_min\_l^{i}
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
\begin{equation} \label{eq:Z_costbarrier} Cost_argumented^{i} = Cost^{i} + penalty_max_l^{i} - deduction_min_l^{i} \end{equation}
9.2.10. Average cost#
%%latexmodelgrab mftt display segment=average_cost
To feed into the main model the average cost is calculated.
This is done on the actual cost, not the argumented cost which can deviate from
the actual cost in order to impose constraints.
\begin{equation}
\label{eq:Average_cost}
Cost\_average = \sum_{i}(Cost^{i} \cdot Share^{i} )
\end{equation}
To feed into the main model the average cost is calculated. This is done on the actual cost, not the argumented cost which can deviate from the actual cost in order to impose constraints.
\begin{equation} \label{eq:Average_cost} Cost_average = \sum_{i}(Cost^{i} \cdot Share^{i} ) \end{equation}
frml <Average_cost> Cost_average = sum(i,Cost__{i}*Share__{i} ) $
LIST I = I : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL /
FOSILE: 1 1 1 0 0 0 0 0 $
LIST J = J : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL $
FRML <AVERAGE_COST> COST_AVERAGE = (COST__OIL*SHARE__OIL +COST__COAL*SHARE__COAL +COST__GAS*SHARE__GAS +COST__BIOMASS*SHARE__BIOMASS +COST__SOLAR*SHARE__SOLAR +COST__WIND*SHARE__WIND +COST__HYDRO*SHARE__HYDRO +COST__GEOTHERMAL*SHARE__GEOTHERMAL ) $
LIST I = I : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL /
FOSILE: 1 1 1 0 0 0 0 0 $
LIST J = J : OIL COAL GAS BIOMASS SOLAR WIND HYDRO GEOTHERMAL $
9.2.11. Max cost#
%%latexmodelgrab mftt ndisplay segment=max_cost
To feed into the main model the max cost is calculated.
This is done on the actual cost, not the argumented cost which can deviate from
the actual cost in order to impose constraints.
\begin{equation}
\label{eq:max_cost}
max\_total = \max_{i}(Share^{i})
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
To feed into the main model the max cost is calculated. This is done on the actual cost, not the argumented cost which can deviate from the actual cost in order to impose constraints.
\begin{equation} \label{eq:max_cost} max_total = \max_{i}(Share^{i}) \end{equation}
9.2.14. Create equations just for fosile fuels#
%%latexmodelgrab mftt ndisplay segment=fosilesharetest
\begin{equation}
\label{eq:SHARES3}
\forall [i=fosile]\:\: fosileshare^{i} = Share^{i}
\end{equation}
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
\begin{equation} \label{eq:SHARES3} \forall [i=fosile]:: fosileshare^{i} = Share^{i} \end{equation}
9.3. Combine all the segments#
%%latexmodelgrab mftt ndisplay render=False
# Combined model
display(Markdown(mftt.equations_latex))
Two lists of technology are defined:
$List ; i ={Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal} \
fosile: { 1 , 1, 1, 0, 0, 0, 0, 0 }$
$List ; j = {Oil, Coal, Gas, Biomass, Solar, Wind, Hydro, Geothermal }$
Any number of technology can be specified (limited by the avaiable memory)
The time index $_t$ is implicit.
Each technology is compared to all other based on the percieved costs and the preferences (choice likelihood) $F^{i,j}$ are calculated.
For all technologies $F^{i,j}+F^{j,i} = 1 $
\begin{equation} \label{eq:preferences} \underbrace{F^{i,j}}_{Preferences} = \frac{1}{ 1+exp( \frac{(Cost_argumented^{i}-Cost_argumented^{j})}{\sigma^{i,j}} )} \end{equation}
\begin{equation} \label{eq:SHARES2} \Delta Share^{i} = \sum_{j}(Share^{i} \times Share^{j} \times (\frac{F^{i,j}}{\tau^{j}} - \frac{F^{j,i}}{\tau^{i}})) \end{equation}
The percieved width in the choice function
\begin{equation} \label{eq:sigma} \sigma^{i,j} = \sqrt{(\sigma^{i})^{(2)} \cdot (\sigma^{j})^{(2)}} \end{equation}
\begin{equation} \label{eq:UD_total} UsefulDemand_total = UsefulDemand_total_{t-1} \cdot (1+\frac{UsefulDemand_total_growth}{100}) \end{equation}
The production from each sector can be calculated. The same goes fdor
\begin{equation} \label{eq:production} Production^{i} = Share^{i} \cdot UsefulDemand_total \end{equation}
\begin{equation} \label{eq:acc_production} Production_accumulated^{i} = Production_accumulated^{i}_{t-1} + Production^{i} \end{equation}
The price of new technology falls in line with its accumulated use through a number of effects.
In princip it depends in global accumulated production. But lacking the data, we just use the local accumulated production. There are many possible functional forms. This is just one example.
\begin{equation} \label{eq:change_production} Change_accumulated_Production^{i} = \frac{Production_accumulated^{i}}{Production_accumulated^{i}_{t-1}} \end{equation}
\begin{equation} \label{eq:price_impact} Cost^{i} = Cost^{i}_{t-1} \cdot (Change_accumulated_Production^{i})^{(-cost_elasticity^{i})} \end{equation}
Sometime there can be constarint (min and/or max) on the shares (or the demand). To enforce constraints
a penalty is added to the percieved cost if the share violate the max constrain.
a deduction is subtracted from the cost if the shares violates the min constrain. .
We really want to have this equations: \begin{equation} \label{eqno:maxout} \underbrace{penalty_max^{i}}_{Penalty_max} = 20 * (Share^{i} > Share_max^{i}) \end{equation}
However in order to get more numerical stability an equation which smooth out the logical expression: $Share^{i} > Share_max^{i}$ is used:
\begin{equation} \label{eq:maxoutlogit} \underbrace{penalty_max_l^{i}}_{Penalty_max} = 1000 * logit^{-1}(1000*(Share^{i} - Share_max^{i})) \end{equation}
We want this \begin{equation} \label{eqno:minout} deduction_min^{i} = Cost^{i}* 0.99 * (Share^{i} < Share_min^{i}) \end{equation}
And implement it like this
\begin{equation} \label{eq:minoutlogit} deduction_min_l^{i} = Cost^{i}* 0.99 * logit^{-1}(100*(Share_min^{i}-Share^{i}) ) \end{equation}
which is the value which enters the equation for prefereences ($F^{i,j}$)
\begin{equation} \label{eq:Z_costbarrier} Cost_argumented^{i} = Cost^{i} + penalty_max_l^{i} - deduction_min_l^{i} \end{equation}
To feed into the main model the average cost is calculated. This is done on the actual cost, not the argumented cost which can deviate from the actual cost in order to impose constraints.
\begin{equation} \label{eq:Average_cost} Cost_average = \sum_{i}(Cost^{i} \cdot Share^{i} ) \end{equation}
To feed into the main model the max cost is calculated. This is done on the actual cost, not the argumented cost which can deviate from the actual cost in order to impose constraints.
\begin{equation} \label{eq:max_cost} max_total = \max_{i}(Share^{i}) \end{equation}
\begin{equation} \label{eq:check_shares} Share_total = \sum_{i}(Share^{i}) \end{equation}
\begin{equation} \label{eq:share_fosile} Share__fosile = \sum_{i=fosile}(Share^{i}) \end{equation}
\begin{equation} \label{eq:SHARES3} \forall [i=fosile]:: fosileshare^{i} = Share^{i} \end{equation}
9.3.1. All phases of the combined model can be displayed:#
if 0:
mftt_latex_model_instance.show
9.4. Create some input data and start values#
%%dataframe startvalues show periods=2 melt t
share_ Production_accumulated_
Oil 0.0828 100
Coal 0.0000 100
Gas 0.0000 100
Biomass 0.0101 100
Solar 0.0085 100
Wind 0.1276 100
Hydro 0.3381 100
Geothermal 0.4329 100
| OIL | COAL | GAS | BIOMASS | SOLAR | WIND | HYDRO | GEOTHERMAL | |
|---|---|---|---|---|---|---|---|---|
| SHARE_ | 0.0828 | 0.0 | 0.0 | 0.0101 | 0.0085 | 0.1276 | 0.3381 | 0.4329 |
| PRODUCTION_ACCUMULATED_ | 100.0000 | 100.0 | 100.0 | 100.0000 | 100.0000 | 100.0000 | 100.0000 | 100.0000 |
| var_name | SHARE__OIL | PRODUCTION_ACCUMULATED__OIL | SHARE__COAL | PRODUCTION_ACCUMULATED__COAL | SHARE__GAS | ... | PRODUCTION_ACCUMULATED__WIND | SHARE__HYDRO | PRODUCTION_ACCUMULATED__HYDRO | SHARE__GEOTHERMAL | PRODUCTION_ACCUMULATED__GEOTHERMAL |
|---|---|---|---|---|---|---|---|---|---|---|---|
| index | |||||||||||
| 2021 | 0.0828 | 100.0 | 0.0 | 100.0 | 0.0 | ... | 100.0 | 0.3381 | 100.0 | 0.4329 | 100.0 |
| 2022 | 0.0828 | 100.0 | 0.0 | 100.0 | 0.0 | ... | 100.0 | 0.3381 | 100.0 | 0.4329 | 100.0 |
2 rows × 16 columns
%%dataframe exoinit nshow periods=100
USEFULDEMAND_TOTAL USEFULDEMAND_TOTAL_GROWTH
100 2
%%dataframe exoparam nshow periods=100 melt
Oil Coal Gas Biomass Solar Wind Hydro Geothermal
Cost_ 83.5 83.5 70.1 134.0 96.9 81.8 108.0 102.5
Sigma_ 28.1 28.1 25.0 106.6 48.4 46.1 77.1 36.0
Tau_ 40.0 40.0 30.0 40.0 25.0 25.0 80.0 40.0
share_max_ 200 200 200 200 200 200 200 200
share_min_ -10 -100 -100 -100 -100 -100 -100 -100
baseline = pd.concat([startvalues_melted,exoparam_melted,exoinit],axis=1).fillna(0).pipe(lambda df:df.loc[:,sorted(df.columns)])
baseline.head().T
| index | 2021 | 2022 | 2023 | 2024 | 2025 |
|---|---|---|---|---|---|
| COST__BIOMASS | 134.0000 | 134.0000 | 134.0 | 134.0 | 134.0 |
| COST__COAL | 83.5000 | 83.5000 | 83.5 | 83.5 | 83.5 |
| COST__GAS | 70.1000 | 70.1000 | 70.1 | 70.1 | 70.1 |
| COST__GEOTHERMAL | 102.5000 | 102.5000 | 102.5 | 102.5 | 102.5 |
| COST__HYDRO | 108.0000 | 108.0000 | 108.0 | 108.0 | 108.0 |
| COST__OIL | 83.5000 | 83.5000 | 83.5 | 83.5 | 83.5 |
| COST__SOLAR | 96.9000 | 96.9000 | 96.9 | 96.9 | 96.9 |
| COST__WIND | 81.8000 | 81.8000 | 81.8 | 81.8 | 81.8 |
| PRODUCTION_ACCUMULATED__BIOMASS | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__COAL | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__GAS | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__GEOTHERMAL | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__HYDRO | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__OIL | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__SOLAR | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| PRODUCTION_ACCUMULATED__WIND | 100.0000 | 100.0000 | 0.0 | 0.0 | 0.0 |
| SHARE_MAX__BIOMASS | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__COAL | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__GAS | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__GEOTHERMAL | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__HYDRO | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__OIL | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__SOLAR | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MAX__WIND | 200.0000 | 200.0000 | 200.0 | 200.0 | 200.0 |
| SHARE_MIN__BIOMASS | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__COAL | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__GAS | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__GEOTHERMAL | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__HYDRO | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__OIL | -10.0000 | -10.0000 | -10.0 | -10.0 | -10.0 |
| SHARE_MIN__SOLAR | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE_MIN__WIND | -100.0000 | -100.0000 | -100.0 | -100.0 | -100.0 |
| SHARE__BIOMASS | 0.0101 | 0.0101 | 0.0 | 0.0 | 0.0 |
| SHARE__COAL | 0.0000 | 0.0000 | 0.0 | 0.0 | 0.0 |
| SHARE__GAS | 0.0000 | 0.0000 | 0.0 | 0.0 | 0.0 |
| SHARE__GEOTHERMAL | 0.4329 | 0.4329 | 0.0 | 0.0 | 0.0 |
| SHARE__HYDRO | 0.3381 | 0.3381 | 0.0 | 0.0 | 0.0 |
| SHARE__OIL | 0.0828 | 0.0828 | 0.0 | 0.0 | 0.0 |
| SHARE__SOLAR | 0.0085 | 0.0085 | 0.0 | 0.0 | 0.0 |
| SHARE__WIND | 0.1276 | 0.1276 | 0.0 | 0.0 | 0.0 |
| SIGMA__BIOMASS | 106.6000 | 106.6000 | 106.6 | 106.6 | 106.6 |
| SIGMA__COAL | 28.1000 | 28.1000 | 28.1 | 28.1 | 28.1 |
| SIGMA__GAS | 25.0000 | 25.0000 | 25.0 | 25.0 | 25.0 |
| SIGMA__GEOTHERMAL | 36.0000 | 36.0000 | 36.0 | 36.0 | 36.0 |
| SIGMA__HYDRO | 77.1000 | 77.1000 | 77.1 | 77.1 | 77.1 |
| SIGMA__OIL | 28.1000 | 28.1000 | 28.1 | 28.1 | 28.1 |
| SIGMA__SOLAR | 48.4000 | 48.4000 | 48.4 | 48.4 | 48.4 |
| SIGMA__WIND | 46.1000 | 46.1000 | 46.1 | 46.1 | 46.1 |
| TAU__BIOMASS | 40.0000 | 40.0000 | 40.0 | 40.0 | 40.0 |
| TAU__COAL | 40.0000 | 40.0000 | 40.0 | 40.0 | 40.0 |
| TAU__GAS | 30.0000 | 30.0000 | 30.0 | 30.0 | 30.0 |
| TAU__GEOTHERMAL | 40.0000 | 40.0000 | 40.0 | 40.0 | 40.0 |
| TAU__HYDRO | 80.0000 | 80.0000 | 80.0 | 80.0 | 80.0 |
| TAU__OIL | 40.0000 | 40.0000 | 40.0 | 40.0 | 40.0 |
| TAU__SOLAR | 25.0000 | 25.0000 | 25.0 | 25.0 | 25.0 |
| TAU__WIND | 25.0000 | 25.0000 | 25.0 | 25.0 | 25.0 |
| USEFULDEMAND_TOTAL | 100.0000 | 100.0000 | 100.0 | 100.0 | 100.0 |
| USEFULDEMAND_TOTAL_GROWTH | 2.0000 | 2.0000 | 2.0 | 2.0 | 2.0 |
9.5. Some housekeeping#
sigma_names = ' '.join(name for name in mftt.exogene if name.startswith('SIGMA'))
tau_names = ' '.join(name for name in mftt.exogene if name.startswith('TAU'))
print(sigma_names)
print(tau_names)
SIGMA__WIND SIGMA__BIOMASS SIGMA__GEOTHERMAL SIGMA__COAL SIGMA__SOLAR SIGMA__HYDRO SIGMA__OIL SIGMA__GAS
TAU__GEOTHERMAL TAU__BIOMASS TAU__COAL TAU__WIND TAU__SOLAR TAU__HYDRO TAU__GAS TAU__OIL
mftt.group_dict = {
'share__[!M]* share_total' : 'Shares',
'c_t* cost*' : 'Cost' ,
'useful*': 'Demand',
'pro*': 'Production',
'deduct*': 'cost deduction for minimum ',
'penal*': 'cost penalty for maximum ',
'*' : 'all'
}
9.6. Make a baseline solution#
mftt.keep_solutions = {} # to clean up with new experiments
res = mftt(baseline,silent=1,first_test=10,init=True,keep='Baseline',alfa=0.1,ljit=0)
9.7. Create some senarios#
mftt.keep_solutions = {} # to clean up with new experiments
lookat = 'hydro'
for change_cost in [0.0 , -10.0, -25.0, -50.0 , 10.0 , 25.0, 50.0]:
alternative = baseline.upd(f'''cost__{lookat} % {change_cost}
share_max__hydro = 0.4
{sigma_names} = 10
{tau_names} = 5
''')
_ = mftt(alternative,keep = f'Cost of {lookat} up {change_cost}%',
alfa=0.1,max_iterations=300,silent=1)
9.8. Display the results#
mftt.keep_show(select_scenario=1)
9.9. Look at the plots of shares#
sharenames = [name for name in mftt.endogene if name.startswith('SHARE__') and not ('_M' in name or '_FOSILE' in name or '_TOTAL' in name)]
mftt[sharenames].df.plot.area();
9.10. Waterfall plots of share changes#
share_out = (100*pd.concat([ pd.DataFrame(df.loc['2120',sharenames] -df.loc['2021',sharenames],columns= [scenario])
for scenario,df in mftt.keep_solutions.items()]
,axis=1).
pipe(lambda df: df.rename({i:i.split('__')[1] for i in df.index})))
display(Markdown(share_out.to_html()))
| Cost of hydro up 0.0% | Cost of hydro up -10.0% | Cost of hydro up -25.0% | Cost of hydro up -50.0% | Cost of hydro up 10.0% | Cost of hydro up 25.0% | Cost of hydro up 50.0% | |
|---|---|---|---|---|---|---|---|
| BIOMASS | -0.9866 | -0.9899 | -0.9940 | -0.9940 | -0.9851 | -0.9843 | -0.9838 |
| GAS | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
| OIL | 16.5962 | 12.9678 | 8.2624 | 8.2117 | 18.1410 | 18.8505 | 19.0183 |
| SOLAR | -0.1726 | -0.2713 | -0.3982 | -0.3993 | -0.1297 | -0.1086 | -0.1013 |
| GEOTHERMAL | -23.3742 | -26.2684 | -29.9775 | -30.0036 | -22.1042 | -21.4650 | -21.2150 |
| HYDRO | -24.7049 | -11.4613 | 5.6788 | 5.8521 | -30.3744 | -33.0246 | -33.7336 |
| WIND | 32.6422 | 26.0231 | 17.4285 | 17.3331 | 35.4524 | 36.7319 | 37.0153 |
| COAL | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
from modelvis import waterplot
fig = waterplot(share_out,title='Change in share from 2020 to 2120',threshold=0.001);
#fig.set_constrained_layout(True)
mftt['production_ac*']
2+2
4